In a large non-reactive pot, combine all the brine ingredients and bring to a simmer. Whisk until the salt and sugar are completely dissolved. Remove from heat and let cool. In a container large enough to hold the shanks, completely submerge them in the cooled brine. Weigh down the shanks with a heavy plate if necessary to keep them fully submerged. Refrigerate overnight.

Preheat oven to 300 degrees.

The next day, remove the shanks from the brine, discarding the liquid. Heat a large Dutch oven over medium-high heat. Pour in enough canola oil to completely coat the bottom of the pot. Dredge the shanks in flour, shaking off any excess. In batches, begin browning the shanks, cooking a few minutes on each side. When browned, transfer the shanks to a plate and begin browning the next batch.

Pour off all but 2 or 3 tablespoons of fat from the pot. Add the celery, carrot, onion and garlic cloves along with a large pinch of salt. Cook the vegetables until tender, about 7 minutes. Add the rosemary and thyme and cook for another minute. Deglaze the pot with the white wine and reduce by three quarters. Add the apple cider and reduce by half. Add the chicken stock and bring the braising liquid up to a simmer. Taste and adjust for seasoning.

Return the shanks to the pot, cover, and place in the oven until the meat is tender, about 4 to 5 hours. Move the shanks from the braising pot to another pot. Strain the braising liquid into the pot with the shanks and allow to cool. Refrigerate overnight.

To serve, reheat the shanks in the liquid. Place the shanks on a platter, spoon over some sauce, and garnish with Shaved Brussels Sprouts.